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anonymous
 5 years ago
if f(x)=2x3 and g(x)=2x^2+1 find
A.f(g(2)) B. g(f(x))
C. does f(x) have and inverse if so find the inverse of f(x)
anonymous
 5 years ago
if f(x)=2x3 and g(x)=2x^2+1 find A.f(g(2)) B. g(f(x)) C. does f(x) have and inverse if so find the inverse of f(x)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0f surely has an inverse because it is a line and therefore one to one.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0f says 'multiply by 2 then subtract 3' so f inverse would say to do the opposite things in the opposite order: add 3 and divide by 2 so \[f^{1}(x)=\frac{x+3}{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if this is confusing, rewrite \[f(x)=2x3\] as \[y = 2x3\] then switch x and y (because that is what the inverse does) to get \[x=2y3\] and solve this for x: \[x=2y3\] \[x+3=2y\] \[\frac{x+3}{2}=y\] and y is your inverse.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is that the answer for C

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok so whats the answers for a and b

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[f(g(x))=f(2x^2+1)=2(2x^2+1)3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i guess there is a little algebra to do now: \[2(2x^2+1)3=4x^2+23=4x^21\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0is it clear what i did? first write \[f(g(x))\] then replace \[g(x)\] by \[2x^2+1\] and then rewrite f replacing \[x\] by \[2x^2+1\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh well if it is \[f(g(2))\] then since \[f(g(x))=4x^21\] then \[f(g(2))=4(2^2)+1=17\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0typo sorry. \[4(2^2)1=15\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or you could say \[g(2)=2(2^2)+1=9\] and \[f(9)=2\times 9  1=15\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[g(f(x))=g(2x3)=2(2x3)^2+1\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this requires more algebra: \[2(2x3)^2+1=2(2x3)(2x3)+1=2(4x^26x+9)+1\] \[=8x^212x+18+1=8x^212x+19\] if my algebra is correct.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok for a how come its 4(2^2)1
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